Speaker: David C. Del Rey Fernández
Affiliation: National Institute of Aerospace and NASA Langley Research Center Hampton, VA
Abstract: Matrix difference operators having the summation by parts (SBP) property have been around since the mid-seventies. The core feature of these operators is that they come equipped with a high-order approximation to integration by parts. In combination with appropriate procedures for weak inter-element coupling and imposition of boundary conditions, the resulting SBP discretization framework allows for a one-to-one correspondence between discrete and continuous stability proofs and thereby naturally guides the construction of robust algorithms. Recently, there have been a number of generalizations and extensions. It is now possible to cast a number of known methods within the SBP framework including discontinuous and continuous Galerkin methods, and the flux-reconstruction method. The SBP concept has been extended to non-tensor nodal distributions applicable to unstructured tetrahedral meshes. Nonlinearly robust schemes can be constructed by enforcing discrete entropy stability on conforming and nonconforming meshes, etc. In this talk, I will give a brief introduction to the SBP concept starting with classical finite-difference SBP operators. I will then show how these ideas can be generalized ending with SBP operators on non-tensor product nodal distributions. I will finish by discussing some ongoing research projects.
Biosketch: Dr. David Del Rey Fernández obtained his PhD in Aerospace Engineering from the University of Toronto Institute for Aerospace Studies in 2015. Currently he is a Postdoctoral Fellow at NIA and NASA Langley Research Center in the Computational AeroScience Branch. His research is focused on the development of flexible and robust high-order numerical methods for the solution of partial differential equations.
Date(s) - Nov 06, 2017
11:00 am - 12:00 pm